Crunching Numbers: Displacement/Length Ratio

We’ve already discussed the basic concept of a boat’s displacement or weight. We’ve also discussed waterline length and how it relates to a boat’s theoretical maximum hull speed. Considered separately, however, length and displacement yield only a general notion of what a boat is like. If you blend the two values you can make a much more nuanced evaluation. The displacement/length ratio (or ...

27th April 2010.
By Charles Doane

Concordia yawl under sail

We’ve already discussed the basic concept of a boat’s displacement or weight. We’ve also discussed waterline length and how it relates to a boat’s theoretical maximum hull speed. Considered separately, however, length and displacement yield only a general notion of what a boat is like. If you blend the two values you can make a much more nuanced evaluation. The displacement/length ratio (or D/L ratio) is the tool yacht designers have created to do this.

To find a boat’s D/L ratio, you first calculate its displacement in long tons (DLT), with 1 long ton equaling 2,240 pounds. Then take the boat’s load waterline length (LWL), multiply it by 0.01, and cube the result. Finally, take this result and divide it into DLT. The complete formula is as follows: D/L = DLT ÷ (0.01 x LWL)³.

As an example, to find the D/L ratio of a 12,000-pound boat with a load waterline length of 28 feet, you first divide 12,000 by 2,240 to find the boat’s displacement in long tons: 12,000 ÷ 2,240 = 5.36 long tons. Then multiply 0.01 by 28 (0.01 x 28 = 0.28) and cube the result (0.28³ = 0.022). Then divide the DLT by this number to find the D/L ratio: 5.36 ÷ 0.022 = 243.6.

A boat with a D/L ratio below 100 is considered ultralight; a D/L value between 100 and 200 is light; 200 to 300 is moderate; 300 to 400 is heavy; and over 400, by modern standards, is very heavy. For a boat of a given length the lower its D/L ratio, the less power it takes to drive the boat to its nominal hull speed and the more likely it is the boat can exceed its hull speed. The 12,000-pound boat in our example above, with its D/L ratio of 244, falls almost exactly in the middle of the range; it needs a moderate amount of power to reach its nominal hull speed of 7.09 knots (1.34 x √28 = 7.09) and stands a reasonable chance of exceeding that speed in some situations.

The higher a boat’s D/L ratio, the more easily it will carry a load and the more comfortable its motion will be. Depending on the sort of cruising you do, these factors may be more important than how fast you are going. Boats with moderate characteristics are generally best suited for cruising, but a “moderate” coastal boat should be lighter than a “moderate” offshore boat. Coastal cruisers carry less gear and supplies and normally sail shorter distances in more protected water. They also benefit more from incremental increases in speed, as they are more likely to sail on a tight schedule and normally seek a safe harbor every night. For this type of sailing I recommend a D/L range of 150 to 300.

Conversely, bluewater cruisers carry more gear and supplies, are sometimes subject to extreme motion in open water, and are less likely to be sailing on a tight schedule. For this type of sailing I recommend D/L ratios between 250 and 400. You can, of course, fiddle these ranges upward or downward according to your own preferences.

When using D/L ratios to evaluate boats, you need to bear in mind that the ratio varies a great deal depending on the displacement value used to calculate it. This is why you need a reasonably realistic displacement number to work with. As we discussed in the displacement post, to get a realistic number you usually need to correct the displacement figure published by the boat’s builder upwards by quite a bit to account for the load the boat normally carries when sailing.

You’ll note that our hypothetical 12,000-pound boat, with its moderate D/L ratio of 244, quickly becomes less moderate as we load it for a cruise. Add Nigel Calder’s minimum recommended displacement correction for light coastal cruising (12,000 + 2,500 = 14,500 lbs.) and the boat’s D/L ratio becomes 294, which nearly qualifies it as a heavy boat. Up the ante even more by loading the boat for heavy coastal or moderate bluewater use (12,000 + 3,750 = 15,750 lbs.) and it moves well into the heavy range with a D/L ratio of 320.

These are not just theoretical increases. Many is the sailor (myself included) who has purchased an empty boat and has reveled in its sprightly performance, only to be demoralized upon discovering how much less sprightly it is when loaded for a serious cruise. The lighter a boat is to begin with (particularly if it is a catamaran), the more dramatic (and demoralizing) this transformation will seem. Most cruisers soon forget how much better their boat sailed before they loaded it with stuff. But if you are devoted to performance you should be draconian when loading your boat and should closely monitor your D/L ratio.

Once you have figured out a boat’s D/L ratio, you can also use that figure to make a more accurate estimate of the boat’s maximum hull speed. I’ll show you how in the next Crunching Numbers post.

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Charles Doane

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Charles Doane is an editor-at-large for SAIL, where he previously was a senior editor. He also served as managing editor at Offshore and associate editor at Cruising World. Charles has logged more than 40,000 miles as an offshore sailor, including six transatlantic passages and some single-handed passages. His blog posts appear courtesy of his website www.WaveTrain.net.
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